2d10 for Skill Checks

[Guest 6801328]

I like the asymmetrical concept of that.

Assuming it's a pass/fall with a DC, here's what it looks like. Can you have no skill? I put in an option for it in black but I'm not sure that's a thing in TOR.

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While the high skills do have a long tail of really high and really low, they group tighter and tighter along the "+3.5 over the last" line.

The part I should have mentioned (had I known somebody was going to model it...) is that a natural 12 on the d12 is an autosuccess, but a 1 is not an autofail.

And, yes, you can still roll with zero skill, which means you have exactly a 1/12 chance of pulling it off.

Other tidbits:
- The GM ("LM") may tell you that the action you want to attempt is not possible. So, no, it's not a 1/12 chance to successfully jump over the moon.
- Even though a 1 on the d12 isn't an autofail, a failure with a 1 on the d12 is sometimes extra special bad.
- If you succeed and get at least one 6 on a d6, that's a "great success". 2 or more 6's is an "extraordinary success". So, of course, not only does more skill increase your chance of success, it also increases your chances of great/extraordinary successes. (The meaning of which varies depending upon what you are trying to do. Sometimes it doesn't mean anything.)
- The game has a mechanic which lets you consume a precious resource to add a fixed number to your roll, after you roll. Because of the probability curve, it's rare that you fail by huge amounts, which means quite frequently even a few additional points are enough to put you over the top. This wouldn't work nearly as well with a flat curve.
- Oh, and sometimes you roll 2d12 and take the better (or lesser). TOR has no official name for this, but rumor has it this is where Mearles got the idea for Advantage/Disadvantage.

So the one dice pool, which again is the core mechanic in the entire game, can produce a big range of results.

 

[Blue]

Given the OP's response to that post, I think those were perfectly fine examples.

They illustrate the exact point he wanted to show by going to a 2d10 system over a d20.

Math doesn't care if the OP likes its or not.

If it's a bad example, it's a bad example. Even if it coincidentally fits someone's feel for what the answer should be.

 

[DND_Reborn]

Math doesn't care if the OP likes its or not.

If it's a bad example, it's a bad example. Even if it coincidentally fits someone's feel for what the answer should be.

Ah, well, since the math is perfect in it, math should still find it to be a perfect example. You might not like it for some strange reason, but hey then that is because you are imperfect.

 

[DEFCON 1]

Au contraire! It's a BEAUTIFUL example! Because I LOVE coincidence! Coincidence is just unrepeated proof! So since I don't need any math proofs to see that what we are doing works, then what we are doing is perfect! You d20 people keep using your outdated die! I SHALL STAY WITH THE TWO TEN-SIDED DICE! AND IT SHALL BE GLORIOUS!

 

[DND_Reborn]

So, basically what you wanted was this...

Original d20 version

A character with a +3 needs 17 or higher for DC 20, or 20% chance of success, a character with +0 needs a 20, only 5%. So, that +3 modifier increases the likelihood of success by 300%.

New 2d10 variant

A character with a +3 needs 17 or higher for DC 20, or 10% chance of success, a character with +0 needs a 20, only 1%. So, that +3 modifier increases the likelihood of success by 900%.

Obviously on the 2d10 variant having a modifier with this DC drastically improves your chances of success over not having a modifier. Of course, since d20 is linear, here you have a better chance of succeeding on the DC just rolling the d20, but that is what you don't want. You want the higher DC's to be harder to make if I followed everything correctly. Now, let's examine the other end of the spectrum...

Original d20 version

A character with a +3 needs 7 or higher for DC 10, or 70% chance of success, a character with +0 needs a 10 or higher, so 55%. So, that +3 modifier increases the likelihood of success by 27.3%.

New 2d10 variant

A character with a +3 needs 7 or higher for DC 10, or 85% chance of success, a character with +0 needs a 10 or higher, so 64%. So, that +3 modifier increases the likelihood of success by 32.8%.

In both situations, the 2d10 variant makes it so the modifier has more impact on the likelihood of success. That was your goal, right?

I don't think these are the best examples.

First, they aren't apples to apples. If you want to see the change, pick your DCs for the first so that both the d20 and 2d10 roll start with the same chance to succeed. Then you can see how they apply. Or at the very least map his DC categories onto default d20 DC categories.

Second, with the DCs given it's more likely that you'll be rolling near the middle. This was a Difficult DC, being made by someone with absolutely no talent (no ability mod, no proficient) and someone likely unskilled but with some natural ability (+3 ability mod) or low level trained but meh suited (+2/+3 proficiency with +1/+0 ability). A difficult DC is more likely to be attempted (intentionally) by someone more suited. All of these will tend toward bringing it towards the middle, where you don't get a 20% to 1% change.

Ok, so let's look at my examples (perfect as they are) and your comments on them. I've underlined key elements for emphasis.

Without either party having a modifier to their roll, the only DC is 12 (both d20 and 2d10 have 45% chance of success). This really doesn't matter to be honest, but you can start with it if you want.

The DCs given have nothing to do with where I'll be rolling. With d20 I have the exact same chance for rolling any number, and as I've shown in an earlier post and others have demonstrated as well, with 2d10 of course I am more likely to roll in the middle--that was the point in using it.

While 20 is a difficult DC, 10 is hardly one.

A DC, difficult or not, will be attempted by whoever needs to make it. This is regardless of level or ability in making the DC. If a party is searching a room for a hidden container and requires a DC 20, someone with no ability might find it when someone with small ability could miss it. If you want to explode the probabilities to the extreme, be my guest but it wasn't necessary to prove the point the OP was trying to achieve.

It is obvious you have some math skills, so prove whatever points you want to as you see fit. If you wanted to expound on my examples to show further emphasis, that would be good and I would have probably commended you for it. Otherwise, you can think (or can you... I wonder sometimes) these are bad examples, but you'd be wrong.

 

[DND_Reborn]

Au contraire! It's a BEAUTIFUL example! Because I LOVE coincidence! Coincidence is just unrepeated proof! So since I don't need any math proofs to see that what we are doing works, then what we are doing is perfect! You d20 people keep using your outdated die! I SHALL STAY WITH THE TWO TEN-SIDED DICE! AND IT SHALL BE GLORIOUS!

Go valiantly forth into the fog of war, bravely holding a d10 in each hand! Cry out, "Come at me, you skill checks of old! I will thrash you soundly with my 2-d-10's, and you shall know the glory of a non-linear distribution!!"

Follow this with a healthy chuckle and slightly crazy look in your eye.

 

[Blue]

Ok, so let's look at my examples (perfect as they are) and your comments on them. I've underlined key elements for emphasis.

The math is correct in your examples. However, that doesn't mean you were plugging in the right numbers.

Without either party having a modifier to their roll, the only DC is 12 (both d20 and 2d10 have 45% chance of success). This really doesn't matter to be honest, but you can start with it if you want.

Actually, these two facts together - the DC and modifier - leads into the most important point. That 2d10 and d20 do not have the same distribution over their length.

Between DC and modifier you determine what you need to roll (or better) on the dice.

I'm going to the rest because it really focuses on only the DC, when my entire point was about why it was a lousy example was about both in tandem. It's an incomplete look at what I was saying that makes so sense without the other half to determine what the roll is. If you thought that was all I was talking about then my apologies for not communicating clearly.

Okay, getting back to the numbers that need to be rolled, this is two components. DC and modifier. The DCs set up by the OP, and expected modifiers for characters, go hand in hand to determine what needs to be rolled. Luckily we can estimate out ranges for both of these.

For intentional tasks, it will likely be done by PCs who are good at what they do. The ranger trained in Survival and with a positive Wisdom mod tracking someone in a forest. The bard trained in persuasion. You get the idea.

Because of the DCs, it ends up that most of the roll-or-better numbers cluster more around the middle of the range. So looking at numbers that are very high is not representative of actual play.

As a matter of fact, since the variation between results is much greater than a d20 in the middle range, and much smaller at the rarely-used 17+ range you were examining, it actually flips the math and shows the opposite of common usage.

So while the math you did was good (I assume, you're good at it), the numbers you were comparing were untypical for actual play and with different distribution then the numbers used more commonly in play.

You mentioned needing a 12 or greater where both have a 45% chance. With your same 3 modifier you used (so needing a 9 or higher), d20 goes to a 60% chance vs 72% chance with 2d10. Hardly the 900% difference between then that the extreme examples found. Even the other way, needing 15 or greater is 30% vs. 21%. Both of those will be more common at the table then 17+ vs. 20+.

 

[DEFCON 1]

So while the math you did was good (I assume, you're good at it), the numbers you were comparing were untypical for actual play and with different distribution then the numbers used more commonly in play.

You mentioned needing a 12 or greater where both have a 45% chance. With your same 3 modifier you used (so needing a 9 or higher), d20 goes to a 60% chance vs 72% chance with 2d10. Hardly the 900% difference between then that the extreme examples found. Even the other way, needing 15 or greater is 30% vs. 21%. Both of those will be more common at the table then 17+ vs. 20+.

Whose play are you talking about?

Considering the fact that this change was for the play at my table (of which you have no idea how often I set DCs at 11, 14, 17, 21 or whatever)... I find it funny that you've been trying to claim my change doesn't work for what I've been trying to accomplish.

Now if you're talking about just the average table... sure your math might be right. But obviously my table isn't average. So why you made the claim in your original post...

Mathematically, you have introduced a much greater variance. You are heading in the opposite direction of your stated goal.

...using math for tables which are not mine makes me cock an eyebrow at your claims.

If all you're trying to do is just say that for the average table that has more DCs in the 10-14 range, rolling 2d10 does not give any appreciable affect... that cool. You probably are right (and if I cared, I'd actually go through your math to confirm it for myself.) But if that's the case, I'm wondering why you also made the statement about my specific situation, which by accounts does not appear to fall into the average table you are talking about (and which is what [MENTION=6987520]dnd4vr[/MENTION] has also been writing about)?

 

[5ekyu]

Whose play are you talking about?

Considering the fact that this change was for the play at my table (of which you have no idea how often I set DCs at 11, 14, 17, 21 or whatever)... I find it funny that you've been trying to claim my change doesn't work for what I've been trying to accomplish.

Now if you're talking about just the average table... sure your math might be right. But obviously my table isn't average. So why you made the claim in your original post...



...using math for tables which are not mine makes me cock an eyebrow at your claims.

If all you're trying to do is just say that for the average table that has more DCs in the 10-14 range, rolling 2d10 does not give any appreciable affect... that cool. You probably are right (and if I cared, I'd actually go through your math to confirm it for myself.) But if that's the case, I'm wondering why you also made the statement about my specific situation, which by accounts does not appear to fall into the average table you are talking about (and which is what [MENTION=6987520]dnd4vr[/MENTION] has also been writing about)?

"Considering the fact that this change was for the play at my table (of which you have no idea how often I set DCs at 11, 14, 17, 21 or whatever)... I find it funny that you've been trying to claim my change doesn't work for what I've been trying to accomplish. "

But, by this logic any change you put forth for **discussion** or analysis on an open forum cannot be addressed by others. If we do not have exact and precise knowledge of what you do at your table then we cannot at all evaluate your proposal to roll 2d10.

For all we know, you only ever assign DC 23.

This sounds like the logic a guy gave me once back in a dice debate some decades ago, about how to calculate average damage from various attacks with various attack rolls using d20s.

His "logic" was that his own persona D20 rolled a 14 more than any other number and so he thought it was perfect math process to use the "mode" not the mean or not the distribution of results. So he based all of his proposals based on the d20 rolling 14.

The key part of this then becomes - the difference between 1d20 and 2d10 distribution is that whether +2 is "more" in 1d20 or 2d10 depends on where on the curve you are. So, if we cannot now assume a "common distribution of Dcs" for analysis, we have now been shut out of any analysis - dont have the tools.

So, hey, when we start from a basis of "ignoring anybody else's DCs and only counting whatever i do ay my table that you guys dont know" the only reasonable reply is to not offer any anlaysis since we dont have any info to go on.

So, basically, thats a wrap.

 

[DND_Reborn]

The math is correct in your examples. However, that doesn't mean you were plugging in the right numbers.

LOL! Sorry I didn't give you my "Dissertation on the Comparative Distributions of Skill Checks Systems: An Examination of the Merits and Flaws of 2d10 versus d20." My point was to simply present a couple examples expounding the differences between the two for a moderate DC 10 and a difficult DC 20. Which was exactly what I accomplished.

Actually, these two facts together - the DC and modifier - leads into the most important point. That 2d10 and d20 do not have the same distribution over their length.

Of course they don't, that is obvious.

Between DC and modifier you determine what you need to roll (or better) on the dice.

I'm going to the rest because it really focuses on only the DC, when my entire point was about why it was a lousy example was about both in tandem. It's an incomplete look at what I was saying that makes so sense without the other half to determine what the roll is. If you thought that was all I was talking about then my apologies for not communicating clearly.

So you want to example the range of DC's over the range of likely applicable modifiers? That's fine, but that wasn't my intent as I felt such an over-analysis was unwarranted. I misunderstood your comment earlier, so apology accepted and I hope you will accept mine.

Okay, getting back to the numbers that need to be rolled, this is two components. DC and modifier. The DCs set up by the OP, and expected modifiers for characters, go hand in hand to determine what needs to be rolled. Luckily we can estimate out ranges for both of these.

For intentional tasks, it will likely be done by PCs who are good at what they do. The ranger trained in Survival and with a positive Wisdom mod tracking someone in a forest. The bard trained in persuasion. You get the idea.

That is very true, but just as often everyone in a party will be involved in a check (such as perception). Other times the best person might not be there.

Because of the DCs, it ends up that most of the roll-or-better numbers cluster more around the middle of the range. So looking at numbers that are very high is not representative of actual play.

As a matter of fact, since the variation between results is much greater than a d20 in the middle range, and much smaller at the rarely-used 17+ range you were examining, it actually flips the math and shows the opposite of common usage.

So while the math you did was good (I assume, you're good at it), the numbers you were comparing were untypical for actual play and with different distribution then the numbers used more commonly in play.

I feel the DCs were appropriate, even if the total modifiers weren't typical for PCs.

You mentioned needing a 12 or greater where both have a 45% chance. With your same 3 modifier you used (so needing a 9 or higher), d20 goes to a 60% chance vs 72% chance with 2d10. Hardly the 900% difference between then that the extreme examples found. Even the other way, needing 15 or greater is 30% vs. 21%. Both of those will be more common at the table then 17+ vs. 20+.

Here, however, you are doing the wrong comparison. I wasn't comparing the difference between 2d10 and d20 directly, I am comparing the two variants by showing the relative increase comparing someone with no modifier to someone with low modifier.

Using the 2d10 variant: For a DC 12, no modifier has a 45% of success. A +3 modifier has a 72% chance for success. That is a 60% relative increase.
Using the d20 model: For a DC 12, no modifier has a 45% of success again. A +3 modifier has a 60% chance for success. That is a 33.3% relative increase.

The point is that the 2d10 variant makes it so having a modifier will greatly increase the relative likelihood of success. You seem to be focusing on the +3 modifiers using the two systems, I'm focusing on comparing two levels of modifiers to each other and then looking at the comparison of the systems.

Perhaps your point is better illustrated with a "moderate" DC 12 and more reasonable PC-type modifiers, say +5 and + 10 (someone with proficiency and some ability versus someone with more proficiency, greater ability and/or expertise):

Using the 2d10 variant: For a DC 12, +5 modifier has a 85% of success. A +10 modifier has a 100% chance for success. That is a 17.6% relative increase.
Using the d20 model: For a DC 12, +5 modifier has only a 70% of success. A +10 modifier has a 95% chance for success. That is a 35.7% relative increase.

So, here the d20 model shows the character with the greater modifier total is more likely to succeed than the lower modifier compared to the 2d10 system. Now, that isn't to say the d20 system itself is more likely, just that the relative comparison of +5 to +10 is.

Was that more in line with your point?